Method for the decoupled control of the quadrature and the resonance frequency of a micro-mechanical rotation rate sensor by means of sigma-delta-modulation

ABSTRACT

A method for the precise measuring operating of a micro-mechanical rotation rate sensor, including at least one seismic mass, at least one drive device for driving the seismic mass in the primary mode (q 1 ) and at least three trimming electrode elements which are jointly associated directly or indirectly with the seismic mass. An electric trimming voltage (u 1 , u 2 , u 3 , u 4 ) is set respectively between the trimming electrode elements and the seismic mass. Each of the electric trimming voltages (u 1 , u 2 , u 3 , u 4 ) are adjusted in accordance with a resonance frequency variable (ũ T , Ũ T,0 ), a quadrature variable (ũ c , Ũ C,0 ) and a restoring variable (ũ S ).

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the U.S. National Phase Application ofPCT/EP2011/054090, filed Mar. 17, 2011, which claims priority to GermanPatent Application No. 10 2010 011 781.1, filed Mar. 17, 2010, thecontents of such applications being incorporated by reference herein.

FIELD OF THE INVENTION

The invention relates to a method according to a method for the precisemeasuring operation of a micro-mechanical rotation rate sensor,comprising at least one seismic mass, at least one drive device fordriving the seismic mass in a primary mode (q₁) and at least threetrimming electrode elements which are jointly associated directly orindirectly with the seismic mass, and to a micro-mechanical rotationrate sensor having at least three trimming electrode elements which arejointly associated with a first seismic mass.

BACKGROUND OF THE INVENTION

It is known that micro-mechanical springs for suspending seismic massesin rotation rate sensors to a certain extent already cause deflectionsin the reading-out direction in the drive mode or primary mode owing torelatively small fabrication inaccuracies which lead, in particular, toundesired edge angles of the respective structures without the presenceof a rotation rate. As a result, interference signals are generatedwhich can be undesirably evaluated as rotation rate signal componentsand therefore falsify the rotation rate signal or cause a measuringerror with respect to the rotation rate signal.

Such undesired edge angles or tilting of springs are process-induced andcan be avoided only to a limited degree. The interference signalsdescribed above, which do not come about owing to a detected rotationrate but rather owing to faulty deflections in the reading-out directionas a function of the deflection of the seismic mass and the springsthereof in the drive direction, are also referred to as quadrature orquadrature signals.

Document WO 03/010492 A1, which is incorporated by reference, proposes amethod for suppressing quadrature signals in a rotation rate sensorwhich comprises two trimming electrode arrangements which are associatedwith a seismic mass, in which method the quadrature of the rotation ratesensor is suppressed by means of the voltage applied to the trimmingelectrodes. However, this quadrature suppression can undesirablyinfluence the resonance frequency of the reading-out mode of therotation rate sensor, as a result of which the differential frequencybetween the resonance frequencies is also changed with respect to thedrive mode or primary mode and the reading-out mode or secondary mode ofthe rotation rate sensor. This is all the more disadvantageous since thevoltage which is applied to the trimming electrodes is includedquadratically in the shifting of the resonance frequency of thereading-out mode.

It is customary that the embodiment of the quadrature of rotation ratesensors of a wafer varies to a relatively high degree owing to processfluctuations and differs to a relatively high degree from one rotationrate sensor to another of a wafer.

Furthermore, it is known to reset the deflection of the seismicmass/masses of a rotation rate sensor with respect to the reading-outmode or secondary mode by means of at least one trimming electrodeelement or a trimming electrode. However, this also usually influencesthe resonance frequency of the secondary oscillator, as well asinfluencing possible quadrature suppression.

BRIEF DESCRIPTION OF THE INVENTION

An aspect of the invention proposes a method for the measuring operationof a rotation rate sensor and a corresponding rotation rate sensor withwhich resetting of the deflection of the secondary mode can be carriedout jointly on the basis of a detected rotation rate, quadraturesuppression and a resonance frequency setting of the secondaryoscillator, in particular in such a way that these three influences canbe implemented or set at least partially independently of one another.

This is achieved according to the invention by means of a method for theprecise measuring operation of a micro-mechanical rotation rate sensor,comprising at least one seismic mass, at least one drive device fordriving the seismic mass in a primary mode (q₁) and at least threetrimming electrode elements which are jointly associated directly orindirectly with the seismic mass, wherein in each case an electrictrimming voltage (u₁, u₂, u₃, u₄) is applied between each of thesetrimming electrode elements and the seismic mass, wherein each of theseelectric trimming voltages (u₁, u₂, u₃, u₄) is set as a function of aresonance frequency manipulated variable (ũ_(T), Ũ_(T,0)), a quadraturemanipulated variable (ũ_(c), Ũ_(C,0)) and a resetting variable (ũ_(S))and a micro-mechanical rotation rate sensor, comprising at least oneseismic mass, at least one drive device for driving the seismic mass inthe primary mode and at least three trimming electrode elements whichare jointly associated directly or indirectly with the seismic mass,wherein in each case an electric trimming voltage is applied betweeneach of these trimming electrode elements and the seismic mass, whereinthe rotation rate sensor is embodied in such a way that it is suitablefor carrying out the method comprising: a method for the precisemeasuring operation of a micro-mechanical rotation rate sensor,comprising at least one seismic mass, at least one drive device fordriving the seismic mass in a primary mode (q₁) and at least threetrimming electrode elements which are jointly associated directly orindirectly with the seismic mass, wherein in each case an electrictrimming voltage (u₁, u₂, u₃, u₄) is applied between each of thesetrimming electrode elements and the seismic mass, wherein each of theseelectric trimming voltages (u₁, u₂, u₃, u₄) is set as a function of aresonance frequency manipulated variable (ũ_(T), Ũ_(T,0)), a quadraturemanipulated variable (ũ_(c), Ũ_(C,0)) and a resetting variable (ũ_(S)).

The method and the rotation rate sensor are preferably embodied ordesigned in such a way that at least the setting of the resonancefrequency can be implemented independently of the resetting of thedeflection of the seismic mass on the basis of a detected rotation rateand the quadrature suppression, and that, in particular, it is alsopossible to set independently of one another the resetting of thedeflection on the basis of a detected rotation rate or the entiredeflection of the at least one seismic mass within the scope of thesecondary mode, and the quadrature suppression.

The quadrature manipulated variable is preferably defined as a staticmanipulated variable for suppressing the deflection or oscillation ofthe secondary mode owing to the quadrature. As a result, in particular,an undesired quadrature signal or a quadrature signal component of theoutput signal of the rotation rate sensor, which is phase-shiftedessentially through 90° or 270° with respect to the component of theoutput signal of the rotation rate sensor which forms the rotation rate,is suppressed.

The resetting manipulated variable is expediently a harmonic oscillationsignal whose amplitude is determined by the output of the firstcontroller unit, wherein this amplitude value is multiplied by aharmonic oscillation signal which has the same frequency as the primarymode or drive mode.

The resonance frequency manipulated variable is preferably defined as astatic variable with which the frequency difference between theresonance frequency of the reading-out mode and the resonance frequencyof the drive mode has substantially a defined value or is adjusted to adefined value or alternatively is preferably essentially zero or isadjusted to zero.

A drive mode or primary mode is preferably understood to be a naturalmode of a rotation rate sensor, preferably the natural oscillation,particularly preferably the oscillation at a resonance frequency of theat least one seismic mass in which the seismic mass of the rotation ratesensor oscillates, in particular, continuously. Quite particularlypreferably, the rotation rate sensor has at least two seismic masseswhich are coupled to one another and which oscillate in anti-phase orare each deflected in the same direction with an inverse orientation toone another in the course of the drive mode.

A reading-out mode or secondary mode is preferably understood to be anatural mode which is preferably set owing to a rotation rate and theassociated effect of the Coriolis force.

It is preferred that the rotation rate sensor comprises at least fourtrimming electrode elements which are jointly associated directly orindirectly with the seismic mass, wherein a first electric trimmingvoltage is applied between the first trimming electrode element and theseismic mass, a second trimming voltage is applied between the secondtrimming electrode element and the seismic mass, a third trimmingvoltage is applied between the third trimming electrode element and theseismic mass, and a fourth trimming voltage is applied between thefourth trimming electrode element and the seismic mass, wherein thefirst trimming voltage u₁, the second trimming voltage u₂, the thirdtrimming voltage u₃ and the fourth trimming voltage u₄ are each setsubstantially with the following dependence of the resonance frequencymanipulated variable ũ_(T), the quadrature manipulated variable ũ_(c)and the resetting variable ũ_(s): u₁=√{square root over(ũ_(T)−ũ_(C)+ũ_(S))}, u₂=√{square root over (ũ_(T)+ũ_(C)−ũ_(S))},u₃=√{square root over (ũ_(T)+ũ_(C)+ũ_(S))}, u₄=√{square root over(ũ_(T)−ũ_(C)−ũ_(S))}.

The resetting variable is alternatively preferably also understood to beŨ_(SD) and/or the resonance frequency manipulated variable to be Ũ_(T,0)and/or the quadrature manipulated variable to be Ũ_(C,0).

The trimming electrode elements are preferably each embodied andarranged in such a way that a capacitance C₁, C₂, C₃ and C₄ is formedbetween the first, second, third and fourth trimming electrode elementand a respectively associated mass electrode element of the associatedseismic mass, with the associated trimming voltage being applied betweenthe trimming electrode element and the mass electrode element, asfollows:

${C_{1} = {ɛ_{0}\frac{A_{1} + {r_{1}t_{1}q_{1}}}{g_{1} - {s_{1}q_{2}}}}},{C_{2} = {ɛ_{0}\frac{A_{2} + {r_{2}t_{2}q_{1}}}{g_{2} + {s_{2}q_{2}}}}},{C_{3} = {ɛ_{0}\frac{A_{3} - {r_{3}t_{3}q_{1}}}{g_{3} - {s_{3}q_{2}}}}},{and}$${C_{4} = {ɛ_{0}\frac{A_{4} - {r_{4}t_{4}q_{1}}}{g_{4} + {s_{4}q_{2}}}}},$where i is in each case an index relating to the numbering of theelectrode elements, g_(i) is the distance over the gap between thetrimming electrode element and the associated mass electrode element inthe undeflected state, A_(i) is the overlapping area between thetrimming electrode element and the associated mass electrode element inthe undeflected state, the product±r_(i) times t_(i) times q₁ is thechange in the overlapping area as a function of the deflection of theprimary mode q₁, wherein t_(i) is the overlapping depth between thetrimming electrode element and the associated mass electrode element andr_(i) is a first positive geometric constant relating to the deflectionof the primary mode q₁, and the product±s_(i) times q₂ is the change inthe distance over the gap between the trimming electrode element and themass electrode element as a function of the deflection of the secondarymode q₂, wherein s_(i) is a second positive geometric constant relatingto the deflection of the secondary mode q₂.

The trimming electrode elements are preferably embodied as planarcapacitor plates which are arranged substantially parallel to the x-yplane of a Cartesian coordinate system. In this context, the deflection,defined by the product±r_(i)*q₁, of the mass electrode elements takesplace, in particular, in the x direction relative to the trimmingelectrode elements. The overlapping depth t_(i) of the trimmingelectrode elements is oriented here in the y direction. The deflectionof the mass electrode elements in the z direction relative to thetrimming electrode elements is particularly preferably oriented in the zdirection.

A_(i), r_(i), t_(i), g_(i) and s_(i) are preferably substantially thesame in all the trimming electrode element/mass electrode element pairs,that is to say A₁=A₂=A₃=A₄, and correspondingly there are respectivelyidentical values for i-th values of r_(i), t_(i), g_(i) and s_(i).

It is preferred that the rotation rate sensor comprises a controlarrangement in which firstly a control error variable is formed from thecontrolled variable with predefinition of a control reference variable,wherein the controlled variable represents the detected deflection ofthe seismic mass in the direction of its secondary mode, and wherein thecontrol reference variable is a harmonic frequency identification signal(y_(D)) with the frequency ω_(s) modulated with the frequency of theprimary mode (ω₁), or such a frequency identification signal issuperimposed on the control reference variable, after which the controlerror variable formed in this way is fed to a first controller unit inwhich at least the resetting variable is generated. In particular, theresetting variable is then demodulated with two harmonic signals,phase-shifted through 90° with respect to one another, in a firstdemodulator unit, as a result of which a quadrature variable and arotation rate variable are acquired, after which a quadrature controlerror variable is generated from the quadrature variable as a functionof a quadrature reference variable, in particular with the value “0”,which quadrature control error variable is fed to a quadraturecontroller unit which makes available the quadrature manipulatedvariable on the output side, and wherein the rotation rate variable orquadrature variable is demodulated in a second demodulator unit with thefrequency ω_(s), as a result of which a frequency variable is acquired,after which a frequency control error variable is generated from thefrequency variable as a function of a frequency reference variable, inparticular with the value “0”, which frequency control error variable isfed to a frequency controller unit which makes available the resonancefrequency manipulated variable ũ_(T) on the output side.

It is expedient that the rotation rate sensor comprises a controlarrangement in which firstly a control error variable is formed from thecontrolled variable with predefinition of a control reference variable,wherein the controlled variable represents the detected deflection ofthe seismic mass in the direction of its secondary mode, and wherein thecontrol reference variable is a harmonic frequency identification signal(y_(D)) with the frequency ω_(s) modulated with the frequency of theprimary mode (ω₁), or such a frequency identification signal issuperimposed on the control reference variable, after which the controlerror variable which is formed in this way is fed to a first controllerunit whose output signal is then demodulated with two harmonic signals,phase-shifted through 90° with respect to one another, in a firstdemodulator unit, as a result of which a quadrature variable and arotation rate variable are acquired, after which a quadrature controlerror variable is generated from the quadrature variable as a functionof a quadrature reference variable, in particular with the value “0”,which quadrature control error variable is fed to a quadraturecontroller unit which makes available the quadrature manipulatedvariable on the output side and wherein the rotation rate variable orquadrature variable is demodulated in a second demodulator unit with thefrequency ω_(s), as a result of which a frequency variable is acquired,after which a frequency control error variable is generated from thefrequency variable as a function of a frequency reference variable, inparticular with the value “0”, which frequency control error variable isfed to a frequency controller unit which makes available the resonancefrequency manipulated variable on the output side.

In particular, the rotation rate sensor has a resetting unit which makesavailable the resetting variable, wherein this resetting variable has,particularly preferably, a defined constant resetting value.

It is preferred that the control arrangement comprises a sigma-deltaconverter with which the controlled variable is digitized directly or atleast a variable dependent thereon is digitized, and after which theresonance frequency manipulated variable, the quadrature manipulatedvariable and the resetting variable are generated as digital variables.

The sigma-delta modulator is embodied, in particular, as anelectro-mechanical sigma-delta modulator.

The sigma-delta modulator particularly preferably comprises acapacitance/voltage converter which is arranged upstream of the firstcontroller unit on the input side, the first controller unit itself, aquantizer which is connected to the latter on the output side, forexample with the sampling frequency f_(s), and a digital/analogconverter and a voltage/force transducer for feeding back the controlprocess.

It is expedient that the output signal of the first controller unit isdigitized, and at least the first demodulator unit, the seconddemodulator unit, the quadrature controller unit and the frequencycontroller unit are embodied in a digital form, and, in particular, inaddition the manipulated variable transformation unit and/or theresetting unit are also embodied in a digital form.

Preferably, in each case two trimming voltages are processed in pairs,in each case by means of one mixer, in each case in pairs as a functionof the digital output signal of the quantizer.

It is preferred that the first and the fourth trimming voltages areprocessed by means of a first mixer (M1), and the second and the thirdtrimming voltages are processed by means of a second mixer (M2), in eachcase as a function of the digital output signal of the quantizer.

The rotation rate sensor, in particular the control arrangement thereof,preferably has a manipulated variable transformation unit which makesavailable the trimming voltages u₁, u₂, u₃ and u₄ as a function of theresonance frequency manipulated variable ũ_(T), the quadraturemanipulated variable ũ_(C) and the resetting variable ũ_(S), inaccordance with the equationsu ₁=√{square root over (ũ _(T) −ũ _(C) +ũ _(S))}, u ₂=√{square root over(ũ _(T) +ũ _(C) −ũ _(S))},u ₃=√{square root over (ũ _(T) +ũ _(C) +ũ _(S))}, u ₄=√{square root over(ũ _(T) −ũ _(C) −ũ _(S))}.

It is preferred that the rotation rate sensor is embodied in such a waythat it can detect rotation rates about at least two different axes,that is to say the rotation rate sensor is of “multi-axis” design.

It is preferred that the first and the second trimming electrodeelements are embodied and arranged in a substantially non-movablefashion, in particular in relation to the respective electrode face ofsaid electrode element, and are electrically insulated and arrangedspaced apart from the seismic mass.

The trimming electrode elements are expediently insulated from oneanother and particularly preferably each of identical design.

The rotation rate sensor expediently has two seismic masses which arecoupled to one another.

It is expedient that the first and the second trimming electrodeelements each have at least one electrode face, which electrode facesare arranged substantially parallel and opposite a trimming face of theseismic mass, and wherein the electrode faces of the first and secondtrimming electrode elements are always associated with a region of thetrimming face lying opposite and/or said electrode faces overlap thisregion, in particular independently of the deflection state of theseismic mass, at least up to a defined amplitude/deflection,particularly preferably even in the case of maximum deflection of theseismic mass. The electrode faces expediently protrude in this casealways beyond the region of the trimming face lying opposite. Theelectrode faces and the trimming face are quite particularly preferablyof substantially planar design.

A micro-mechanical rotation rate sensor is preferably understood to be amicro-mechanical gyroscope.

An aspect of the invention also relates to the use of the rotation ratesensor in motor vehicles, in particular in a motor vehicle controlsystem.

The method according to an aspect of the invention and the rotation ratesensor according to an aspect of the invention can be used in differentregions for detecting one or more rotation rates and/or by means ofcorresponding signal processing for detecting one or more rotationalaccelerations. In this context, their use is preferred in vehicles, inparticular in motor vehicles and aircraft, in automation technology, innavigation systems, in image stabilizers of cameras, in industrialrobotics and in games consoles, and particularly preferably in therespective corresponding control systems in this context. The use of themethod and of the rotation rate sensor in/as yaw rate sensor/sensorsand/or in/as yaw acceleration sensor/sensors in a motor vehicle controlsystem such as, for example, ESP, is quite particularly preferred.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best understood from the following detailed descriptionwhen read in connection with the accompanying drawing.

In the drawing, in each case in a schematic illustration, FIG. 1 showsan exemplary embodiment of a capacitor formed from a trimming electrodeelement, which is positionally fixed with respect to the sensor housing,and from a mass electrode element which is connected to the seismic massor is embodied as a part thereof,

FIG. 2 shows an exemplary embodiment of a method or rotation rate sensorin which a frequency identification signal is predefined as a harmonicsetpoint value upstream of the first controller and before demodulationas a reference variable of the controlled variable,

FIG. 3 shows an exemplary model of a 1-bit electro-mechanicalsigma-delta modulator with a sensor and filter structure or firstcontroller,

FIG. 4 shows an exemplary illustration of a simplified control circuit,

FIG. 5 shows an illustration of a simplified spectrum of anelectro-mechanical sigma-delta modulator,

FIG. 6 a) shows an exemplary multi-bit feedback to an electrode and b)shows a single-bit feedback via a plurality of electrodes,

FIG. 7 shows exemplary reading circuits with a) a single-ended designand b) a differential design, and

FIG. 8 shows an exemplary embodiment of a method or rotation rate sensorwith predefinition of a frequency identification signal as a harmonicsetpoint value for the controlled variable, by means of sigma-deltamodulation.

DETAILED DESCRIPTION OF THE INVENTION

The exemplary capacitor which is illustrated in FIG. 1 and is composedof a trimming electrode element 1 and a mass electrode element 2 is as aparallel-plate capacitor, wherein the distance or the distance g_(i)over the gap is embodied in the z direction between the two electrodes,and the deflection of the mass electrode element in the primary modeoccurs in the x direction, wherein the change in the overlapping areaoccurs in the x direction, and the deflection of the mass electrodeelement in the secondary mode occurs in the z direction.

FIG. 2 illustrates an exemplary method or an exemplary rotation ratesensor comprising a control arrangement 3 in which firstly a controlerror variable is formed from the controlled variable y withpredefinition of a control reference variable y_(D), wherein thecontrolled variable y represents the detected deflection of the seismicmass in the direction of its secondary mode, and wherein the controlreference variable is a harmonic frequency identification signal withthe frequency ω_(s) modulated with the frequency of the primary mode ω₁,after which the control error variable which is formed in this way isfed to a first controller unit 4 in which the resetting variable ũ_(S)is generated.

The resetting variable ũ_(S) is, on the one hand, fed directly to themanipulated variable transformation unit 7 and, furthermore, theresetting variable ũ_(S) is demodulated with two harmonic signals,phase-shifted through 90° with respect to one another, in a firstdemodulator unit 5, as a result of which a quadrature variable ũ_(S,S)and a rotation rate variable ũ_(S,C) are acquired, jointly symbolized asũ_(S), after which a quadrature control error variable is generated fromthe quadrature variable u_(S,S) as a function of a quadrature referencevariable, in particular with the value “0”, which quadrature controlerror variable is fed to a quadrature controller unit 10 which makesavailable the quadrature manipulated variable ũ_(c), or referred to hereas ũ_(C,0), on the output side, and wherein the rotation rate variableũ_(S,C) demodulated in a second demodulator unit 8 with the frequencyω_(s), as a result of which a frequency variable ũ_(S,CC) is acquired,after which a frequency control error variable is generated from thefrequency variable as a function of a frequency reference variable, inparticular with the value “0”, which frequency control error variable isfed to a frequency controller unit 9 which makes available the resonancefrequency manipulated variable ũ_(T), referred to here as ũ_(T,)0, onthe output side. The rotation rate variable Ũ_(S,C) is alsolow-pass-filtered and forms the output signal Ũ_(S,C0) of the sensorwhich contains the information about the detected rotation rate.

The manipulated variable transformation unit 7 makes available thetrimming voltages u₁, u₂, u₃ and u₄, in accordance with the equationsu ₁=√{square root over (ũ _(T) −ũ _(C) +ũ _(S))}, u ₂=√{square root over(ũ _(T) +ũ _(C) −ũ _(S))},u ₃=√{square root over (ũ _(T) +ũ _(C) +ũ _(S))}, u ₄=√{square root over(ũ _(T) −ũ _(C) −ũ _(S))}.

FIG. 8 illustrates the rotation rate sensor and therefore also thecorresponding method using the sigma-delta modulator. In this context,the rotation rate sensor comprises a control arrangement 3 in whichfirstly a control error variable is formed from the controlled variabley with predefinition of a control reference variable, wherein thecontrolled variable y represents the detected deflection of the seismicmass in the direction of its secondary mode, and wherein the controlreference variable is a harmonic frequency identification signal withthe frequency ω_(s) modulated with the frequency of the primary mode ω₁,after which the control error variable formed in this way is fed to afirst controller unit 4 whose output signal is then digitized in aquantizer 12 with the clock frequency f_(s) and the bit sequence whichis generated as a result is subsequently demodulated in a digitalfashion with two harmonic signals, phase-shifted through 90° withrespect to one another, in a first digital demodulator unit 5, as aresult of which a quadrature variable ũ_(S,S) and a rotation ratevariable ũ_(S,C) are acquired, after which a quadrature control errorvariable is generated from the quadrature variable as a function of aquadrature reference variable, in particular with the value “0”, whichquadrature control error variable is fed to a quadrature controller unit10 which makes available the quadrature manipulated variable ũ_(C),referred to here as ũ_(C,0), on the output side.

The rotation rate variable ũ_(S,C) is demodulated in a seconddemodulator unit 8 with the frequency ω_(s), as a result of which afrequency variable Ũ_(S,CC) is acquired, after which a frequency controlerror variable is generated from the frequency variable as a function ofa frequency reference variable, in particular with the value “0”, whichfrequency control error variable is fed to a frequency controller unit 9which makes available the resonance frequency manipulated variablereferred to here as Ũ_(T,)0, on the output side. The rotation ratevariable Ũ_(S,C) is also low-pass-filtered and forms the output signalŨ_(S,C0) of the sensor which contains the information about the detectedrotation rate.

Furthermore, the rotation rate sensor comprises a resetting unit 11which makes available the resetting variable Ũ_(SD), for example as adefined constant resetting value.

The control arrangement comprises, for example, a sigma-delta converterwith which the controlled variable is digitized and after which theresonance frequency manipulated variable, the quadrature manipulatedvariable and the resetting variable are generated as digital variables.The sigma-delta modulator, embodied as an electro-mechanical sigma-deltamodulator, comprises here a capacitance/voltage converter 13 which isarranged upstream of the first controller unit 4 on the input side, thefirst controller unit 4 itself, a quantizer 12 which is connected to thelatter on the output side and having the sampling frequency f_(s), and adigital/analog converter (not illustrated) and a voltage/forcetransducer (not illustrated) for feeding back the control process.

The first and the fourth trimming voltages U₁, U₄ are processed by meansof a first mixer M1, and the second and the third trimming voltages U₂,U₃ are processed by means of a second mixer M2, each as a function ofthe digital output signal of the quantizer 12.

A description and analysis will be given below by way of example bymeans of mathematical illustrations:

Typically, micro-electro-mechanical rotation rate sensors have twoweakly damped mechanical vibration modes which are orthogonal withrespect to one another, the so-called primary and secondary modes, whichare coupled by means of the Coriolis effect when a rotation rate occurs.As a result of inaccuracies due to manufacture, further couplinggenerally occurs between the primary and secondary modes, unbalanceeffect or quadrature. However, in the output signal of the sensor, thesignal components have a phase difference of 90° owing to the Coriolisand unbalance effects. As a result of corresponding demodulation, theoutput signal can accordingly be decomposed into a rotation ratecomponent and a quadrature component. The conventional control conceptof micro-mechanical rotation rate sensors therefore typically comprisesa quadrature controller which compensates the signal component owing tothe unbalance effect by using an additional actuator system. Any offsetdrifting of the rotation rate component in the output signal owing todemodulation errors can thereby be avoided. In order to increasesensitivity, generally extremely weakly damped mechanical structures areused. The resulting slow dynamic response behavior of the sensor owingto a rotation rate can be improved by compensating the rotation ratecomponent using further suitable actuators in a resetting controller(also referred to as locking mode). The desired sensor dynamics are thendefined by the closed circuit of the resetting controller. The maximumsensitivity of the rotation rate sensor is achieved if the resonancefrequencies of the primary and secondary modes are identical. Since thechange in sensitivity is already very large in the vicinity of thisworking point when there are small parameter deviations, it is necessaryto control the resonance frequency. The present invention preferablydeals with the design of an overall control concept which comprises thequadrature controller, resetting controller and frequency controller.

The sensor type on which this invention is based is expediently acapacitive rotation rate sensor. In this context, the excitation and thereading out of the primary and secondary oscillations are carried out bymeans of capacitive actuators and sensors. For the rest it will beassumed that, by using suitable capacitive actuators or drive devices,the rotation rate sensor in the primary mode is made to oscillateharmonically with a constant amplitude. The frequency of the oscillationcorresponds here to the resonance frequency of the primary mode. If itis also assumed that the amplitude and frequency of the primaryoscillation are adjusted ideally to a constant setpoint value, thereaction of the secondary oscillation on the primary oscillation can beignored and the movement differential equation of the secondary mode canbe written in the formm ₂ {umlaut over (q)} ₂ +d ₂ {dot over (q)} ₂ +k ₂ q ₂ =f ₂(q ₁ ,q ₂ ,u₁ , . . . ,u _(m))+Ωc ₂₁ {dot over (q)} ₁ −k ₂₁ q ₁  (1)

Here, q₁ and q₂ denote the primary and secondary modes, Ω denotes therotation rate and u₁, . . . , u_(m) denote the voltages at thecapacitive actuators for influencing the secondary mode. The positiveconstants m₂, d₂ and k₂ correspond to the coefficient of inertia, thedamping coefficient and the rigidity coefficient, while the constantsc₂₁ and k₂₁, which can assume both positive and negative values,correspond to the coupling terms owing to the Coriolis effect andunbalance effect. The nonlinear input term f₂(q₁, q₂, u₁, . . . , u_(m))depends on the arrangement of the capacitive actuators. Ifparallel-plate capacitors are assumed, as shown in FIG. 1, they can bedesigned in such a way that both harmonic excitation of the secondarymode and compensation of the coupling term k₂₁q₁ are possible byapplying a constant voltage component. In addition, the constantcomponent causes the resonance frequency of the secondary mode to beinherently influenced. Firstly, it is assumed that only parallel-platecapacitors with rectangular electrodes are considered. Given a number ofm capacitive actuators of this type, FIG. 1 shows the i-th actuator,i=1, . . . , m, composed of an electrode which is rigidly connected tothe housing and of a movable electrode. The movable electrode has thetranslatory degrees of freedom x_(i) and where x_(i) and z_(i) describethe movement of the center point of the movable electrode in thedirection of the primary mode or of the secondary mode, that is to sayif no other modes are excited the following applies x_(i)=±r_(i)q₁ andz_(i)=±s_(iq2) with the positive constants r_(i) and s_(i). Thecapacitance C_(i) and the stored energy W_(p,i) of the i-th actuator arethen obtained as:

$\begin{matrix}{\mspace{79mu}{{C_{i} = {{ɛ_{0}\frac{A_{i} + {x_{i}}}{g_{i} - z_{i}}} = {ɛ_{0}\frac{A_{i} \pm {r_{i}q_{1}}}{g_{i} \pm {s_{i}q_{2}}}}}},{= {\frac{1}{2}C_{i}u_{i}^{2}}}}} & (2)\end{matrix}$with the electrical voltage u_(i), the dielectric constant ∈₀, the gapg_(i), the overlapping length l_(i), the depth t_(i) and the overlappingarea A_(i)=l_(i)t_(i) in the nondistorted state. The entire impressedforce of the capacitive actuators, f₂ in (1), is calculated as follows

$\begin{matrix}{{= {= {{\mp \frac{1}{2}}u_{i}^{2}}}},\mspace{20mu}{{f_{2}\left( {q_{1},q_{2},u_{1},\ldots\mspace{14mu},u_{m}} \right)} = {\sum\limits_{i = 1}^{m}\;}}} & (3)\end{matrix}$

Equations (2) and (3) show that, depending on the geometric arrangementof the capacitive actuator, a force effect can be applied to thesecondary mode which has four different sign permutations, specificallyfor x_(i)=±r_(i)q₁ and z_(i)=±s_(i)q₂.

If it is firstly assumed that there are precisely four capacitiveactuators, which have different sign permutations, the following appliesfor the force acting on the secondary mode

$\begin{matrix}{f_{2} = {\frac{ɛ_{0}}{2}{\left( {{\frac{s_{1}\left( {A_{1} + {r_{1}t_{1}q_{1}}} \right)}{\left( {g_{1} - {s_{1}q_{2}}} \right)^{2}}u_{1}^{2}} - {\frac{s_{2}\left( {A_{2} + {r_{2}t_{2}q_{1}}} \right)}{\left( {g_{2} + {s_{2}q_{2}}} \right)^{2}}u_{2}^{2}} + {\frac{s_{3}\left( {A_{3} - {r_{3}t_{3}q_{1}}} \right)}{\left( {g_{3} - {s_{3}q_{2}}} \right)^{2}}u_{3}^{2}} - {\frac{s_{4}\left( {A_{4} - {r_{4}t_{4}q_{1}}} \right)}{\left( {g_{4} + {s_{4}q_{2}}} \right)^{2}}u_{4}^{2}}} \right).}}} & (4)\end{matrix}$

One preferred embodiment of the control concept is then the inputvariable transformationu ₁=√{square root over (ũ _(T) −ũ _(C) +ũ _(S))}, u ₂=√{square root over(ũ _(T) +ũ _(C) −ũ _(S))},u ₃=√{square root over (ũ _(T) +ũ _(C) +ũ _(S))}, u ₄=√{square root over(ũ _(T) −ũ _(C) −ũ _(S))}  (5)

If the transformation (5) is inserted in (4) and if the expression f₂ islinearized according to q₁ and q₂ about the working point q₂=0 and q₂=0,an approximate relationship is obtained which is valid for smalldeflections. Assuming that the gap for all the parallel-plate capacitorsis of equal size, i.e. g=g_(j), and the following geometricrelationships are met sA=s_(j)A_(j), rst=r_(j)s_(j)t_(j) and s²A=s_(j)²A_(j) for j=1, . . . , m, which can be interpreted as symmetryconditions for the weighted overlapping areas and overlapping lengths,the linear approximation is obtained in the form

⁢f 2 ≅ 2 ⁢ ɛ 0 ⁢ s j ⁢ A j g 2 ︸ b 2 ⁢ u ~ s - 2 ⁢ ɛ 0 ⁢ r j ⁢ s j ⁢ t 1 g 2 ︸ ⁢q 1 ⁢ u ~ c + 4 ⁢ ɛ 0 ⁢ s j 2 ⁢ A j g 3 ︸ k 2 , T ⁢ ⁢ q 2 ⁢ u ~ T . ( 6 )

Equation (6) shows that the transformed input variables are nowdecoupled from one another. Equation (1) can now be written in the formm ₂ {umlaut over (q)} ₂ +d ₂ {dot over (q)} ₂+(k ₂ −k _(2,T) ũ _(T))q ₂=b ₂ ũ _(S) +Ωc ₂₁ {dot over (q)} ₁−(k ₂₁ +k _(21,C) ũ _(C))q ₁  (7)

It is directly apparent in (7) that the input ũ_(S) can be used forharmonically exciting the secondary mode, the input ũ_(C) forcompensating the unbalance and the input ũ_(T) for trimming theresonance frequency of the secondary mode.

In what has been stated above, the restrictive assumption was made thatall the capacitive actuators have rectangular electrodes and do not havedegrees of rotational freedom.

The above concept can now be very easily extended to electrodes of anydesired shape which can be formed from a finite number of sufficientlysmall rectangular elements. Assuming a division into sufficiently smallelements, it is therefore also possible to approximate the force effectof rotating electrodes of any desired shape, in the above form.Furthermore, it is assumed that the finite actuator elements arecombined to form four groups k=1, . . . , 4 with the number m_(K) ofelements with the common sign permutation and are supplied with thevoltage u_(K). If the distributed actuators satisfy the geometricconditions

$\mspace{20mu}{{{sA} = {{\sum\limits_{j = 1}^{m_{1}}\;{s_{1,j}A_{1,j}}} = {{\sum\limits_{j = 1}^{m_{2}}\;{s_{2,j}A_{2,j}}} = {{\sum\limits_{j = 1}^{m_{3}}\;{s_{3,j}A_{3,j}}} = {\sum\limits_{j = 1}^{m_{4}}\;{s_{4,j}A_{4,j}}}}}}},{{rst} = {{\sum\limits_{j = 1}^{m_{1}}\;{r_{1,j}s_{1,j}t_{1,j}}} = {{\sum\limits_{j = 1}^{m_{2}}\;{r_{2,j}s_{2,j}t_{2,j}}} = {{\sum\limits_{j = 1}^{m_{3}}\;{r_{3,j}s_{3,j}t_{3,j}}} = {\sum\limits_{j = 1}^{m_{4}}\;{r_{4,j}s_{4,j}t_{4,j}}}}}}},\mspace{20mu}{{s^{2}A} = {{\sum\limits_{j = 1}^{m_{1}}\;{s_{1,j}^{2}A_{1,j}}} = {{\sum\limits_{j = 1}^{m_{2}}\;{s_{2,j}^{2}A_{2,j}}} = {{\sum\limits_{j = 1}^{m_{3}}\;{s_{3,j}^{2}A_{3,j}}} = {\sum\limits_{j = 1}^{m_{4}}\;{s_{4,j}^{2}{A_{4,j}.}}}}}}}}$then the entire force acting on the secondary mode where

$\mspace{20mu}{{b_{2} = {2\frac{ɛ_{0}}{g^{2}}{sA}}},{{k_{21,C}} = {2\frac{ɛ_{0}}{g^{2}}{rst}}},{{k_{2,T}} = {4\frac{ɛ_{0}}{g^{3}}s^{2}A}}}$can in turn be approximated in the form (6).

For the actual exemplary controller design, use is made of what isreferred to as an envelope curve model which describes the dynamics ofthe Fourier coefficients of the system variables. To do this, it isfirstly assumed that the primary mode experiences a harmonic oscillationin the form q₁=Ω_(1,S) sin(ω₁t) with the constant amplitude Q_(1,S) andthe frequency ω₁, which corresponds to the natural frequency of theprimary mode. Furthermore, it is assumed that the secondary mode can beformed as a harmonic oscillation of the form q₂=Q_(2,S) sin(ω₁t)+Q_(2,C)cos(ω₁t). In the case of harmonic excitation with the inputũ_(S)=Ũ_(S,C) cos(ω₁t) and the constant inputs ũ_(T)=Ũ_(T,0) andũ_(C)=Ũ_(C,0), the dynamics of the Fourier coefficients Q_(2,S) andQ_(2,C) can be described using the differential equation system

$\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{bmatrix}Q_{2,s} \\Q_{2,c}\end{bmatrix}} = {\begin{bmatrix}\alpha_{2} & {\omega_{1} - \omega_{2}} \\{{- \omega_{1}} + \omega_{2}} & \alpha_{2}\end{bmatrix}{\quad{\begin{bmatrix}Q_{2,s} \\Q_{2,c}\end{bmatrix} + \begin{bmatrix}{{\beta_{21}\Omega} - {\beta_{2}{\overset{\sim}{U}}_{s,c}}} \\{{\beta_{21}\left( {\Gamma_{M} + {\Gamma_{c}{\overset{\sim}{U}}_{c,0}}} \right)} + {\beta_{2}{\overset{\sim}{U}}_{s,s}}}\end{bmatrix}}}}} & (8)\end{matrix}$with the damping parameter and the natural frequency of the secondarymode

$\begin{matrix}{{\alpha_{2} = {{- \frac{1}{2}}\frac{d_{2}}{m_{2}}}},{\omega_{2} = \sqrt{\frac{k_{2} - {k_{2,T}{\overset{\sim}{U}}_{T,0}}}{m_{2}} - \alpha_{2}^{2}}}} & (9)\end{matrix}$as well as the input and unbalance parameters

$\begin{matrix}{{\beta_{2} = {\frac{1}{2}\frac{b_{2}}{m_{2}\omega_{2}}}},{\beta_{21} = {\frac{1}{2}\frac{\omega_{1}}{\omega_{2}}\frac{c_{21}}{m_{2}}Q_{1,s}}},{\Gamma_{M} = \frac{k_{21}}{\omega_{1}c_{21}}},{\Gamma_{c} = \frac{k_{21\; c}}{\omega_{1}c_{21}}}} & (10)\end{matrix}$and the inputs Ũ_(T,0), Ũ_(C,0), Ũ_(S,S) and Ũ_(S,C). In the text whichfollows, the harmonically oscillating system variables (q₂, ũ_(s), . . .) are denoted as “fast” signals and the associated Fourier coefficients(Q_(2,S), Q_(2,C), Ũ_(S,S), Ũ_(S,C), . . . ) are denoted as “slow”signals.

For the operation of the rotation rate sensor, it is possible todifferentiate between the so-called “split mode” and the “matched mode”.In the split mode operation, the input Ũ_(T,0) is constant and theabsolute value of the difference between the frequencies assumes aconstant value |ω₁−ω₂|>>1. Since the change in the sensitivity owing todifferent damping parameters d₂ and therefore α₂ does not play asignificant role for a sufficiently large frequency difference, it isnot necessary to control the secondary natural frequency and offlineidentification of the parameters α₂ and ω₁−ω₂ is sufficient. On theother hand, in the matched mode operation, a frequency interval ω₁−ω₂→0which is as small as possible is aimed at. The change in sensitivity hasits maximum in the vicinity of the point ω₁=ω₂, for which reasonfrequency control and online identification of the frequency intervalω₁−ω₂ are unavoidable.

Since the output signal y=c₂q₂ is used both for resetting the unknownrotation rate and for compensating the unknown unbalance, no furtherinformation, for example about the frequency difference, can be acquiredfrom the output signal. For this purpose, there is a need for additionalexcitation of the secondary mode which contains frequency components inthe spectrum which are different from the natural frequency ω₁. Apossibility which can be implemented easily is harmonic excitation withthe frequency ω_(s)=ω₁/l and l>>1.

If input variables of the envelope curve model (8) of the formŨ_(S,S)=Ũ_(S,S0)+Ũ_(S,SS) sin(ω_(S)t)+U_(S,SC) cos(ω_(S)t) andŨ_(S,C)=Ũ_(S,C0)+Ũ_(S,CS) sin(ω_(S)t)+Ũ_(S,CC) cos(ω_(S)t) as well ascorresponding state variables Q_(2,S)=Q_(2,S0)+Q_(2,SS)sin(ω_(S)t)+Q_(2,SC) cos(ω_(S)t) and Q_(2,C)=Q_(2,C0)+Q_(2,CS)sin(ω_(S)t)+Q_(2,CC) cos(ω_(S)t) are thus assumed, it is possible, byignoring the coupling terms relating to the primary mode, to specify thedynamics of the new Fourier coefficients Q_(2,SS), Q_(2,SC), Q_(2,CS)and Q_(2,CC) (SC subsystem) by means of an envelope curve model of theform

$\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{bmatrix}Q_{2,{ss}} \\Q_{2,{sc}} \\Q_{2,{cs}} \\Q_{2,{cc}}\end{bmatrix}} = {\begin{bmatrix}\alpha_{2} & \omega_{s} & {\omega_{1} - \omega_{2}} & 0 \\{- \omega_{s}} & \alpha_{2} & 0 & {\omega_{1} - \omega_{2}} \\{{- \omega_{1}} + \omega_{2}} & 0 & \alpha_{2} & \omega_{s} \\0 & {{- \omega_{1}} + \omega_{2}} & {- \omega_{s}} & \alpha_{2}\end{bmatrix}{\quad{\begin{bmatrix}Q_{2,{ss}} \\Q_{2,{sc}} \\Q_{2,{cs}} \\Q_{2,{cc}}\end{bmatrix} + {{\begin{bmatrix}0 & 0 & {- \beta_{2}} & 0 \\0 & 0 & 0 & {- \beta_{2}} \\\beta_{2} & 0 & 0 & 0 \\0 & \beta_{2} & 0 & 0\end{bmatrix}\begin{bmatrix}{\overset{\sim}{U}}_{s\;,{ss}} \\{\overset{\sim}{U}}_{s\;,{sc}} \\{\overset{\sim}{U}}_{s\;,{cs}} \\{\overset{\sim}{U}}_{s\;,{cc}}\end{bmatrix}}.}}}}} & (11)\end{matrix}$

The dynamics of the Fourier coefficients Q_(2,S0) and Q_(2,C0) (0subsystem) is described by the envelope curve model

$\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}\begin{bmatrix}Q_{2,{sc}} \\Q_{2,{c\; 0}}\end{bmatrix}} = {\begin{bmatrix}\alpha_{2} & {\omega_{1} - \omega_{2}} \\{{- \omega_{1}} + \omega_{2}} & \alpha_{2}\end{bmatrix}{\quad{\begin{bmatrix}Q_{2,{s\; 0}} \\Q_{2,{c\; 0}}\end{bmatrix} - \begin{bmatrix}{{\beta_{21}\Omega} - {\beta_{1}{\overset{\sim}{U}}_{s\;,{c\; 0}}}} \\{{\beta_{21}\left( {\Gamma_{M} + {\Gamma_{c}{\overset{\sim}{U}}_{c\;,0}}} \right)} + {\beta_{2}{\overset{\sim}{U}}_{s\;,{s\; 0}}}}\end{bmatrix}}}}} & (12)\end{matrix}$

It is now assumed below that the “fast” output signal y=c₂q₂ is adjustedby means of a robust controller R_(R)(B) to a harmonic setpoint valuey_(D)=Y*_(CC) cos(ω_(S)t)cos(ω₁t) where ω_(S)=ω₁/l and l>>1. If it isfirstly assumed that this subordinate resetting control is ideal and theoutput y precisely follows the setpoint value y_(D), that is to say thefollowing applies: Q_(2,SS)=0, Q_(2,SC)=0, Q_(2,CS)=0 andQ_(2,CC)=Y_(CC)/C₂, the input variable U_(S)=[Ũ_(S,S) Ũ_(S,C)] in thesteady state is obtained from equation (11) and equation (12) in theform

$\begin{matrix}{{{\overset{\sim}{U}}_{s\;,c} = {\underset{\underset{{\overset{\sim}{U}}_{s\;,{c\; 0}}}{︸}}{\frac{\beta_{21}}{\beta_{2}}\Omega} + {\underset{\underset{{\overset{\sim}{U}}_{s\;,{cc}}}{︸}}{\frac{\omega_{1} - \omega_{2}}{\beta_{2}c_{2}}Y_{cc}^{\prime}}{\cos\left( {\omega_{s}t} \right)}}}},{{\overset{\sim}{U}}_{ss} = {{- \frac{\Gamma_{M}}{\underset{\underset{{\overset{\sim}{U}}_{s\;,{s\; 0}}}{︸}}{\Gamma_{C}}}} - {\underset{\underset{{\overset{\sim}{U}}_{s\;,{ss}}}{︸}}{\frac{\omega_{s}}{\beta_{2}c_{2}}Y_{cc}^{\prime}}{\sin\left( {\omega_{s}t} \right)}} - {\underset{\underset{{\overset{\sim}{U}}_{s\;,{sc}}}{︸}}{\frac{\alpha_{2}}{\beta_{2}c_{2}}Y_{cc}^{\prime}}{{\cos\left( {\omega_{s}t} \right)}.}}}}} & (13)\end{matrix}$

The individual components Ũ_(S,C0), Ũ_(S,CC) and Ũ_(S,S0) can beacquired by demodulating the manipulated variable ũ_(S), as is shown inFIG. 2. The Fourier coefficient Ũ_(S,C0) in (13) is proportional to therotation rate and therefore serves as an output of the rotation ratesensor.

The actual quadrature control is then carried out by compensating thevariable Ũ_(S,S0) by means of the input variable Ũ_(C,0). The distancefrom the input Ũ_(C,0) to the output Ũ_(S,S0) which is used as the basisfor the design of the quadrature controller R_(Q)(s) is given by thesteady-state relationship

$\begin{matrix}{= {- {\frac{\beta_{21}\Gamma_{M}}{\beta_{2}}.}}} & (14)\end{matrix}$

Furthermore, from (13) it is apparent that the Fourier coefficientŨ_(S,CC) is linearly dependent on the frequency difference ω₁−ω₂. Thefrequency difference can therefore be calculated in the formω₁−ω₂=Ũ_(S,CC)β₂c₂/Y*_(CC) The frequency controller then has thefunction of adjusting the Fourier coefficient Ũ_(S,CC) to zero. Thetransmission function, serving as a basis for the frequency control withthe controller R_(F)(s), of the distance from the input Ũ_(T,0) to theoutput Ũ_(S,CC), which is linearized about the working point ω₁=ω₂, isgiven by the steady-state relationship

$\begin{matrix}{\mspace{79mu}{G_{s} = {\left. \frac{\partial{\overset{\sim}{U}}_{s\;,{cc}}}{\partial{\overset{\sim}{U}}_{T\;,0}} \right|_{\omega_{1} = \omega_{2}} = {{- \frac{1}{2}}\frac{k_{2\; T}}{\beta_{2}c_{2}m_{2}\omega_{1}}Y_{cc}^{\prime}}}}} & (15)\end{matrix}$The associated cascaded control structure is illustrated in FIG. 2.

In reality, the transmission function of the closed circuit of thesubordinate resetting controller is not precisely equal to 1. Theresponse to the defined harmonic setpoint value then has a phase shiftω₀ and change A₀ in amplitude in the steady state which can be correctedin the subsequent demodulation by demodulating with A₀ cos(ω_(S)t+φ₀)instead of cos(ω_(S)t).

The exemplary reading out of a sensor by means of an electro-mechanicalsigma-delta (SD) modulator in the locking mode (resetting controller)provides a large number of advantages over conventional reading systemswithout locked operation. As a result of the locked operation, it ispossible, inter alia, to improve the bandwidth, the dynamic range andthe linearity. The design of an electro-mechanical SD modulator is shownin FIG. 3 and is composed of a sensor, the capacitance/voltage converter(C/V), the filter or the first controller unit R_(R)(s), whichcorresponds to the resetting controller described above, a quantizerwith a sampling frequency f_(S), the digital/analog converter (DAC) anda voltage/force transducer (−F/V). The stability of the closed circuitis brought about by suitable dimensioning of the filter. In FIG. 4, asimplified control circuit is shown with an input F_(in), a transmissionfunction H(s), which models the system comprised of the sensor andfilter R_(R)(s), the quantization noise e and an output D₀ which is fedback. The output signal for the closed circuit is obtained in theLaplace space as

$\begin{matrix}{\mspace{79mu}{D_{0} = {{F_{in}\frac{1}{\underset{\underset{STF}{︸}}{1 + \frac{1}{H(s)}}}} + {e{\frac{1}{\underset{NTF}{\underset{︸}{1 + {H(s)}}}}.}}}}} & (16)\end{matrix}$

By means of the signal transmission function (STF) and the noisetransmission function (NTF) in (16) it is possible to determine thatlarge amplification of the filter is desirable in the signal band inorder, on the one hand, to transmit the input signal F_(in) with one tothe output D₀ (e.g. it is then possible to assume an ideal resettingcontrol (y=y_(D)) for the rest of the controller design, as explainedabove) and, on the other hand, to suppress the quantization noise. Inthe case of rotation rate sensors, a band pass filter can preferably beused with a resonance frequency which corresponds to the primaryresonance frequency of the rotation rate sensor. FIG. 5 shows a spectrumof the SD modulator presented. Two local minimums can be determined inthe spectrum; the right-hand one results from the band pass filter andthe left-hand one from the transmission function of the rotation ratesensor owing to the secondary mode. Here, it is immediately apparentthat the quality can be considerably improved if the two local minimumslie one on top of the other.

In the case of the SD modulator, the digital output signal is fed backto the sensor element via a DAC. The linearity of the sensor is improvedby the active feedback. This causes the measurement signal at the inputto be compensated as much as possible, so that in the ideal case thesensor has a negligible differential signal. In the case of the SDprinciple, the statement should be modified to the effect that thesignal which is to be measured is compensated on average, and the faultonly acts on the sensor as an input signal. The use of multi-bitsolutions permits the variance between the input signal and outputsignal to be reduced, thereby improving the quality of the overallsystem with respect to linearity. The feedback is carried outcapacitively via a pulse-width-modulated signal, a single or multi-bitvoltage signal or a single or multi-bit charge signal. The multi-bitfeedback can be obtained either by means of a specific D/A converter,which carries out implicit linearization of the feedback force, as inFIG. 6a , or by using a plurality of feedback electrodes, as can be seenin FIG. 6 b.

Using SD converters with continuous timing allows the powering to besignificantly reduced. This is possible since the RC technology requiressmaller bandwidths for the operational amplifiers (OPV). Compared to theswitch/capacitor technology, this may be a bandwidth which is smaller bya factor of up to 10. As a result, the current consumption can also bereduced by the same factor. For the evaluation circuit with continuoustiming it is possible to select two different approaches. The first isbased on tapping the signal from the center electrode, as can be seen inFIG. 7a . This approach provides the advantage that only one amplifieris required for the evaluation circuit. Disadvantages of this method arethe complicated generation of the modulation signal, which should bephase-shifted through precisely 180°, and that as a result of thefeedback no additional signals can be transmitted to the centerelectrode. For these reasons, a fully differential design is alsofrequently selected which does not have the abovementioned disadvantagesand is illustrated in FIG. 7b . As a third alternative, a dedicatedamplifier can be selected for each capacitor. However, this results in alarge number of amplifiers and increases the chip surface.

In this section, the control concept presented above and the sigma-deltamodulator are combined to form a further exemplary embodiment which isillustrated with respect to FIG. 8. In the digital control block, thesignal ũ_(S) is replaced by ũ_(SD). The signal ũ_(SD) defines the forcefeedback of the sigma-delta modulator and can be set to a constantvalue. The three different manipulated variables ũ_(SD), Ũ_(C,0) andŨ_(T,0) are prevented from influencing one another by means of the inputvariable transformation described. The four voltages u₁₊, u²⁻, u₃₊, andu⁴⁻ are impressed, via the mixers M1 and M2, on the correspondingelectrodes of the capacitive actuators of the rotation rate sensor.Here, u₁₊ and u⁴⁻ as well as u²⁻ and u₃₊ are the same with respect tothe manipulated variables Ũ_(C,0) and Ũ_(T,0) and differ only in theforce feedback value ũ_(SD). The sigma-delta modulator is composed of acapacitance/voltage converter (C/V), a loop filter (R_(R)(s)), a 1-bitquantizer, which is clocked with a sampling frequency f_(s), and a forcefeedback (DAC) defined by the two mixers M1 and M2. The two mixers M1and M2 are actuated with the output signal of the sigma-delta modulator.The force feedback acting on the sensor by means of the voltages u₁, u₂,u₃ and u₄ therefore occurs as a result of switching over between thecurrent levels of the signals u₁₊ and u⁴⁻ or u²⁻ and u₃₊.

As a result of the combination of the quadrature controller andfrequency controller as well as the sigma-delta modulator it is possibleto combine the advantages of the respective concepts, as described byway of example in the sections above.

One particularly advantageous feature of the method and of the rotationrate sensor is the nonlinear input variable transformation (5) as wellas the use of an electro-mechanical sigma-delta modulator withcontinuous timing.

The use of the SD converter with continuous timing for reading outsensors brings a wide variety of advantages. The first advantage is thereduced power consumption compared to the switch/capacitor technology.As a result of the fact that signals with continuous timing are used,the operational amplifiers which are used require less bandwidth up to afactor of 10, and therefore less current up to a factor of 10. Thisleads to drastically lower energy consumption, which plays a particularrole especially in the strongly growing market of mobile sensor systems.Furthermore, SD converters with continuous timing have an implicitanti-aliasing filter, which filters frequencies above f_(s)/2. Althoughthe sensor already has a low-pass behavior, it does not sufficientlyreduce frequencies above the Nyquist frequency, and the properties ofthis filter cannot be freely adjusted either. The properties of SDconverters with continuous timing reduce the expenditure on circuitryand the costs as well as the necessary power consumption. Furthermore,the lack of cyclical recharging of the reading electrodes on the testmass results in a smaller reading force, which leads to an increase inthe signal-to-noise interval and therefore to improved resolution.

Conventional methods for controlling the secondary resonance frequencyof capacitive rotation rate sensors dispense with the compensation ofinherent quadratic input nonlinearity. If a quadrature controller and/orresetting controller is required for the operation of the rotation ratesensor, this results in the frequency controller, quadrature controllerand resetting controller influencing one another. Since, in particularin the case of a resetting controller, the output signal of the rotationrate sensor corresponds to the required manipulated variable forresetting the rotation rate, the problem occurs here that the outputvariable of the rotation rate sensor is influenced directly by thefrequency controller. If the secondary resonance frequency thereforechanges, for example owing to temperature influences, and the frequencycontroller compensates the resulting control error, a change occurs inthe output signal also. This undesired effect can be avoided by theproposed input variable transformation with the result that complicatedcorrections by means of characteristic curve fields are not necessary.

The frequency controller, quadrature controller and resetting controllercan be designed independently of one another for the completelydecoupled overall system with the new, transformed input variables(ũ_(T), ũ_(C) and ũ_(S)). The proposed control concept has the advantagethat there is no longer a need for demodulation of the output signal andtherefore no longer a need for decoupling of the quadrature signal androtation rate signal provided that the “fast” resetting controller isconfigured to be sufficiently robust with respect to changes inparameter (in particular of the secondary resonance frequency).Decomposition into a quadrature component and rotation rate component iseffected by demodulation of the manipulated variable of the resettingcontroller. Furthermore, the proposed control concept has the advantageof a linear relationship between the resonance frequency and theassociated measurement signal (Ũ_(S,CC)=Y*_(2,CC)(ω₁−ω₂)/(β₂c₂)) andtherefore enables a stable influence zone of any desired size for thefrequency controller.

The invention claimed is:
 1. A method for the precise measuringoperation of a micro-mechanical rotation rate sensor, comprising atleast one seismic mass, at least one drive device for driving theseismic mass in a primary mode (q₁) and at least four trimming electrodeelements which are jointly associated directly or indirectly with theseismic mass, wherein in each case an electric trimming voltage (u₁, u₂,u₃, u₄) is applied between each of these trimming electrode elements andthe seismic mass, wherein the rotation rate sensor comprises a controlarrangement to measure rotation rate, and wherein the controlarrangement comprises a sigma-delta converter with which a controlledvariable (y) representing the detected deflection of the seismic mass inits secondary mode (q₂) is digitized directly or at least a variabledependent thereon is digitized, and after which: 1) a resetting variable(ũ_(S)) is generated as a digital variable, and 2) both a resonancefrequency manipulated variable (ũ_(T)), and a quadrature manipulatedvariable (ũ_(C)) are generated as digital variables based on the digitalresetting variable (ũ_(S)), and wherein each of the electric trimmingvoltages (u₁, u₂, u₃, u₄) is set as a function of a square root of adifferent sum of the digitized resonance frequency manipulated variable(ũ_(T)), the quadrature manipulated variable (ũ_(C)) and anotherresetting variable (ũ_(S)).
 2. The method as claimed in claim 1, whereinthe rotation rate sensor comprises at least four trimming electrodeelements which are jointly associated directly or indirectly with theseismic mass, wherein a first electric trimming voltage is appliedbetween the first trimming electrode element and the seismic mass, asecond trimming voltage is applied between the second trimming electrodeelement and the seismic mass, a third trimming voltage is appliedbetween the third trimming electrode element and the seismic mass, and afourth trimming voltage is applied between the fourth trimming electrodeelement and the seismic mass, wherein the first trimming voltage u₁, thesecond trimming voltage u₂, the third trimming voltage u₃ and the fourthtrimming voltage u₄ are each set substantially with the followingdependence of the resonance frequency manipulated variable ũ_(T), thequadrature manipulated variable ũ_(C) and the resetting variable ũ_(S):u ₁=√{square root over (ũ _(T) −ũ _(C) +ũ _(S))}, u ₂=√{square root over(ũ _(T) +ũ _(C) −ũ _(S))},u ₃=√{square root over (ũ _(T) +ũ _(C) +ũ _(S))}, u ₄=√{square root over(ũ _(T) −ũ _(C) −ũ _(S))}.
 3. The method as claimed in claim 1, whereinthe trimming electrode elements are each embodied and arranged in such away that a capacitance C₁, C₂, C₃ and C₄ is formed between the first,second, third and fourth trimming electrode element and a respectivelyassociated mass electrode element of the associated seismic mass, withthe associated trimming voltage being applied between the trimmingelectrode element and the mass electrode element, as follows:${C_{1} = {ɛ_{0}\frac{A_{1} + {r_{1}t_{1}q_{1}}}{g_{1} - {s_{1}q_{2}}}}},{C_{2} = {ɛ_{0}\frac{A_{2} + {r_{2}t_{2}q_{1}}}{g_{2} + {s_{2}q_{2}}}}},{C_{3} = {ɛ_{0}\frac{A_{3} - {r_{3}t_{3}q_{1}}}{g_{3} - {s_{3}q_{2}}}}}$and${C_{4} = {ɛ_{0}\frac{A_{4} - {r_{4}t_{4}q_{1}}}{g_{4} + {s_{4}q_{2}}}}},$where i is in each case an index relating to the numbering of theelectrode elements, g_(i) is the distance over the gap between thetrimming electrode element and the associated mass electrode element inthe undeflected state, A_(i) is the overlapping area between thetrimming electrode element and the associated mass electrode element inthe undeflected state, the product±r_(i) times t_(i) times q₁ is thechange in the overlapping area as a function of the deflection of theprimary mode q₁, wherein t_(i) is the overlapping depth between thetrimming electrode element and the associated mass electrode element andr_(i) is a first positive geometric constant relating to the deflectionof the primary mode q₁, and the product±s_(i) times q₂ is the change inthe distance over the gap between the trimming electrode element and themass electrode element as a function of the deflection of the secondarymode q₂, wherein s_(i) is a second positive geometric constant relatingto the deflection of the secondary mode q₂.
 4. The method as claimed inclaim 3, wherein A_(i), r_(i), t_(i), g_(i) and s_(i) are substantiallythe same in all the trimming electrode element/mass electrode elementpairs.
 5. The method as claimed in claim 1, wherein the controlarrangement firstly forms a control error variable from the controlledvariable (y) with predefinition of a control reference variable, whereinthe controlled variable (y) represents the detected deflection of theseismic mass in the direction of its secondary mode, and wherein thecontrol reference variable is a harmonic frequency identification signal(y_(D)) with the frequency ω_(s) modulated with the frequency of theprimary mode (ω₁), or such a frequency identification signal issuperimposed on the control reference variable, after which the controlerror variable formed in this way is fed to a first controller unit inwhich at least the resetting variable (ũ_(S)) is generated.
 6. Themethod as claimed in claim 5, wherein the resetting variable (ũ_(S)) isthen demodulated with two harmonic signals, phase-shifted through 90°with respect to one another, in a first demodulator unit, as a result ofwhich a quadrature variable and a rotation rate variable are acquired,after which a quadrature control error variable is generated from thequadrature variable as a function of a quadrature reference variable,which quadrature control error variable is fed to a quadraturecontroller unit which makes available the quadrature manipulatedvariable (ũ_(C)) on the output side, and wherein the rotation ratevariable or quadrature variable is demodulated in a second demodulatorunit with the frequency ω_(s), as a result of which a frequency variableis acquired, after which a frequency control error variable is generatedfrom the frequency variable as a function of a frequency referencevariable, which frequency control error variable is fed to a frequencycontroller unit which makes available the resonance frequencymanipulated variable (ũ_(T)) on the output side.
 7. The method asclaimed in claim 1, wherein the control arrangement firstly forms acontrol error variable from the controlled variable (y) withpredefinition of a control reference variable, wherein the controlledvariable (y) represents the detected deflection of the seismic mass inthe direction of its secondary mode, and wherein the control referencevariable is a harmonic frequency identification signal (y_(D)) with thefrequency ω_(s) modulated with the frequency of the primary mode (ω₁),or such a frequency identification signal is superimposed on the controlreference variable, after which the control error variable which isformed in this way is fed to a first controller unit whose output signalis then demodulated with two harmonic signals, phase-shifted through 90°with respect to one another, in a first demodulator unit, as a result ofwhich a quadrature variable and a rotation rate variable are acquired,after which a quadrature control error variable is generated from thequadrature variable as a function of a quadrature reference variable,which quadrature control error variable is fed to a quadraturecontroller unit which makes available the quadrature manipulatedvariable (ũ_(C)) on the output side and wherein the rotation ratevariable or quadrature variable is demodulated in a second demodulatorunit with the frequency ω_(s), as a result of which a frequency variableis acquired, after which a frequency control error variable is generatedfrom the frequency variable as a function of a frequency referencevariable, which frequency control error variable is fed to a frequencycontroller unit which makes available the resonance frequencymanipulated variable (ũ_(T)) on the output side.
 8. The method asclaimed in claim 7, wherein the rotation rate sensor has a resettingunit which makes available the resetting variable (ũ_(S)), wherein thisresetting variable (ũ_(S)) has a defined constant resetting value. 9.The method as claimed in claim 7, wherein the output signal of the firstcontroller unit is digitized, and at least the first demodulator unit,the second demodulator unit, the quadrature controller unit and thefrequency controller unit are embodied in a digital form, and, inaddition at least one of a manipulated variable transformation unit anda resetting unit are also embodied in a digital form.
 10. The method asclaimed in claim 1, wherein the sigma-delta converter is embodied as anelectro-mechanical sigma-delta converter.
 11. The method as claimed inclaim 10, wherein the sigma-delta converter comprises acapacitance/voltage converter which is arranged upstream of the firstcontroller unit on the input side, the first controller unit itself, aquantizer which is connected to the latter on the output side, and adigital/analog converter and a voltage/force transducer for feeding backthe control process.
 12. The method as claimed in claim 11, wherein ineach case two trimming voltages are processed in pairs (u₁, u₄), (u₂,u₃), in each case by means of one mixer (M1, M2), in each case in pairsas a function of the digital output signal of the quantizer.
 13. Themethod as claimed in claim 1, wherein the control arrangement of therotation rate sensor, has a manipulated variable transformation unitwhich makes available the trimming voltages u₁, u₂, u₃ and u₄ as afunction of the resonance frequency manipulated variable ũ_(T), thequadrature manipulated variable ũ_(C) and the resetting variable ũ_(S),in accordance with the equations u₁=√{square root over(ũ_(T)−ũ_(C)+ũ_(S))}, u₂=√{square root over (ũ_(T)+ũ_(C)−ũ_(S))},u₃=√{square root over (ũ_(T)+ũ_(C)+ũ_(S))}, u₄=√{square root over(ũ_(T)−ũ_(C)−ũ_(S))}.
 14. A micro-mechanical rotation rate sensor,comprising at least one seismic mass, at least one drive device fordriving the seismic mass in the primary mode and at least three trimmingelectrode elements which are jointly associated directly or indirectlywith the seismic mass, wherein in each case an electric trimming voltageis applied between each of these trimming electrode elements and theseismic mass, wherein the rotation rate sensor is embodied in such a waythat it is suitable for carrying out the method comprising: a method forthe precise measuring operation of a micro-mechanical rotation ratesensor, comprising at least one seismic mass, at least one drive devicefor driving the seismic mass in a primary mode (q₁) and at least threetrimming electrode elements which are jointly associated directly orindirectly with the seismic mass, wherein in each case an electrictrimming voltage (u₁, u₂, u₃, u₄) is applied between each of thesetrimming electrode elements and the seismic mass, wherein the rotationrate sensor comprises a control arrangement to measure rotation rate,and wherein the control arrangement comprises a sigma-delta converterwith which a controlled variable (y) representing the detecteddeflection of the seismic mass in its secondary mode (q₂) is digitizeddirectly or at least a variable dependent thereon is digitized, andafter which: 1) and a resetting variable (ũ_(S)) is generated as adigital variable, and 2) both a resonance frequency manipulated variable(ũ_(T)), and a quadrature manipulated variable (ũ_(C)) are generated asdigital variables based on the digital resetting variable (ũ_(S)), andwherein each of the electric trimming voltages (u₁, u₂, u₃, u₄) is setas a function of a square root of a different sum of the digitizedresonance frequency manipulated variable (ũ_(T)), the quadraturemanipulated variable (ũ_(C)) and another resetting variable (ũ_(S)). 15.A method for the precise measuring operation of a micro-mechanicalrotation rate sensor, comprising at least one seismic mass, at least onedrive device for driving the seismic mass in a primary mode (q₁) and atleast three trimming electrode elements which are jointly associateddirectly or indirectly with the seismic mass, wherein in each case anelectric trimming voltage (u₁, u₂, u₃, u₄) is applied between each ofthese trimming electrode elements and the seismic mass, wherein each ofthese electric trimming voltages (u₁, u₂, u₃, u₄) is set as a functionof a resonance frequency manipulated variable (ũ_(T)), a quadraturemanipulated variable (ũ_(C)) and a resetting variable (ũ_(S)); whereinthe rotation rate sensor comprises a control arrangement to measure arotation rate, and wherein the control arrangement comprises asigma-delta converter with which a controlled variable (y) representingthe detected deflection of the seismic mass in its secondary mode (q₂)is digitized directly or at least a variable dependent thereon isdigitized, and after which the resonance frequency manipulated variable(ũ_(T)), the quadrature manipulated variable (ũ_(C)) and the resettingvariable (ũ_(S)) are generated as digital variables, and wherein thecontrol arrangement firstly forms a control error variable from thecontrolled variable (y) with predefinition of a control referencevariable, wherein the controlled variable (y) represents the detecteddeflection of the seismic mass in the direction of its secondary mode,and wherein the control reference variable is a harmonic frequencyidentification signal (y_(D)) with the frequency ω_(s) modulated withthe frequency of the primary mode (ω₁), or such a frequencyidentification signal is superimposed on the control reference variable,after which the control error variable formed in this way is fed to afirst controller unit in which at least the resetting variable (ũ_(S))is generated.